Isogeometric collocation methods, Mathematical Models and Methods in Applied Sciences, vol.20, issue.11, pp.2075-2107, 2010. ,
A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, 2012. ,
Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes, Math. Models Methods Appl. Sci, vol.16, issue.07, pp.1031-1090, 2006. ,
Some estimates for h-p-k-refinement in isogeometric analysis, Numerische Mathematik, vol.118, pp.271-305, 2011. ,
Algorithms for numerical analysis in high dimensions, SIAM Journal on Scientific Computing, vol.26, issue.6, pp.2133-2159, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-02076682
Finite elements: Theory, fast solvers and applications in solid mechanics, 2007. ,
Estimation of linear functionals on sobolev spaces with application to Fourier transforms and spline interpolation, SIAM Journal on Numerical Analysis, vol.7, issue.1, pp.112-124, 1970. ,
The Mathematical Theory of Finite Element Methods, 2002. ,
The choice of quadrature in NURBS-based isogeometric analysis, Proc. of the 3rd South-East European Conference on Computational Mechanics (SEECCM), 2013. ,
Computation of quadrature rules for integration with respect to refinable functions on fixed nodes, 2014. ,
Finite Element Method for Elliptic Problems, Society for Industrial and Applied Mathematics, 2002. ,
Subdivision surfaces: A new paradigm for thin-shell finite-element analysis, Int. J. Numer. Meth. Engrg, vol.47, pp.2039-2072, 2000. ,
Quasi-interpolation in isogeometric analysis based on generalized B-splines, Computer Aided Geometric Design, vol.27, issue.8, pp.656-668, 2010. ,
Isogeometric Analysis: Toward Integration of CAD and FEA, 2009. ,
Efficient computer manipulation of tensor products, ACM Trans. Math. Softw, vol.5, issue.2, pp.173-182, 1979. ,
A practical guide to splines; rev, 2001. ,
Curves and surfaces for CAGD: a practical guide, 2002. ,
THB-splines: The truncated basis for hierarchical splines, Computer Aided Geometric Design, vol.29, pp.485-498, 2012. ,
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models, Journal of Computational Physics, vol.262, issue.0, pp.153-171, 2014. ,
Some quadrature rules for Galerkin methods using B-spline basis functions, Computer Methods in Applied Mechanics and Engineering, vol.19, issue.3, pp.401-416, 1979. ,
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.4135-4195, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-01513346
Efficient quadrature for NURBS-based isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.58, pp.301-313, 2010. ,
Computation of the isogeometric analysis stiffness matrix on GPU, Proc. of the 3rd South-East European Conference on Computational Mechanics (SEECCM), 2013. ,
GPU accelerated computation of the isogeometric analysis stiffness matrix, Computer Methods in Applied Mechanics and Engineering, vol.269, issue.0, pp.334-355, 2014. ,
Goal-adaptive isogeometric analysis with hierarchical splines, Computer Methods in Applied Mechanics and Engineering, vol.270, issue.0, pp.270-292, 2014. ,
Exploring matrix generation strategies in isogeometric analysis, Mathematical Methods for Curves and Surfaces, vol.8177, pp.364-382, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00816141
Study of computational efficiency of numerical quadrature schemes in the isogeometric analysis, Proc. of the 18 th Int'l Conf. Engineering Mechanics, EM'12, pp.1135-1143, 2012. ,
An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and t-spline CAD surfaces, Computer Methods in Applied Mechanics and Engineering, vol.249252, issue.0, pp.116-150, 2012. ,
Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations, Computer Methods in Applied Mechanics and Engineering, vol.267, pp.170-232, 2013. ,
Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.277, issue.0, pp.1-45, 2014. ,
, Spline Functions: Basic Theory, 2007.
Approximation in the finite element method, Numerische Mathematik, vol.19, pp.81-98, 1972. ,
An Analysis of the Finite Element Method, 1973. ,
A hierarchical approach to adaptive local refinement in isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.4952, pp.3554-3567, 2011. ,